Apparently, the proposed method can generate point-specific activation map which uncovers more fine-grained information than Grad-CAM. We will further show the relationship between our overall activation map and Grad-CAM. As another way for generating overall activation map on more complex architectures, Grad-CAM follows a heuristic design without a clear meaning for the generated map. When we calculate the activation map based on Grad-CAM, what do we get? [1]} has shown that Grad-CAM is equivalent to CAM on GAP based architecture, while it is not true on other architectures. For a classification architecture with flattened feature and one FC layer, the prediction score for class \(c\)  is formulated as \(S_{c}=\sum _{i,j,k}W_{i,j,k,c}A_{i,j,k}\) , where \(W\)  is the reshaped weights of the FC layer following the shape of the last convolutional feature (\(A\) ). From our activation decomposition perspective, the contribution of each position \((i,j)\)  is clearly given by \(\sum _{k}W_{i,j,k,c}A_{i,j,k}\) , while the Grad-CAM map for class \(c\)  at \((i,j)\)  position is given by:
\(\begin{split}GradCAM_{i,j,c} & = \sum _{k} A_{i,j,k}GAP\left(\frac{\partial S_{c}}{\partial A_{k}}\right)\\& =\sum _{k} A_{i,j,k}GAP\left(W_{k}\right).\end{split}\) 
